The specific heats, CP and CV of a gas of diatomic molecules, A, are… | JEE Main 2019 (9 Apr, Shift 2)

Q51JEE Main 2019 · 9 APR · SHIFT 2Medium

Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation

The specific heats, CP and CV of a gas of diatomic molecules, A, are given (in units of J mol–1 K–1) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

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Answer: (b)

Rigid diatomic: $C_V = \dfrac{5}{2}R \approx 20.8$ J/mol K; a vibrational mode raises it towards $\dfrac{7}{2}R \approx 29$ .
Gas A: $C_V = 22 > 20.8$ , so extra energy goes into vibration: A has a vibrational mode.
Gas B: $C_V = 21 \approx \dfrac{5}{2}R$ , so B is rigid.
So the answer is (b) A has a vibrational mode but B has none.

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Specific Heats of Gases - Cp, Cv, γ & Mayer's Relation question from JEE Main 2019 (9 Apr, Shift 2)

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